It is beneficial to be able to monitor various parameters in wells, and to communicate accumulated parameter data to surface or another remote location. For example, if a section of a well has been abandoned, it can be useful to know whether there is cross-flow between perforations, or leakage or invasion of fluids in the abandoned section. In another example, flow, cement and casing integrity, etc., could be monitored in a producing section of a well. Therefore, it will be appreciated that improvements are continually needed in the art of well monitoring.